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Aliases
Subgroups
160 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 169 points:
(1,2,4,8,5,10,16,24,6,9,17,23,18,25,31,32)(3,11,13,27,14,20,29,22,12,26,15,30,28,7,19,21)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169);(1,3)(2,7,9,20)(4,15)(5,14)(6,12)(8,22,23,21)(10,11,25,26)(13,17)(16,19)(18,28)(24,30,32,27)(29,31);(3,12)(7,20)(11,26)(13,15)(14,28)(19,29)(21,22)(27,30)
Conjugacy classes & character table
6028 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 842);
Finite Group Databasebeta